Question: I have a multi-stage testing procedure using items drawn from a pre-calibrated item bank. Each stage gives each person a measure and standard error. Can I combine these measures to give each person an overall measure?
Answer: The most exact answer would be to use all of a person's responses to all stages to estimate a new measure - but this may not be practical. Typically the first-stage is a short, wide subtest. The later stages may be narrower, longer subtests. So raw score performance and measurement precision can vary greatly between the subtests. RMT 8:3 p. 376, suggests that a useful combined measure is obtained by standard error weighting the subtest measures:
If it is reasonable to think of all subtests as measuring this same fixed effect, then its standard error approximates 1 / sqrt( Σ ( 1 / SE subtest ² ) ).
Summing multiple measures. J.M. Linacre 17:2 p. 925
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
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